Just before Stuart Broad bowled the second over, two protesters from Just Stop Oil ran out of the Grandstand and onto the outfield, sprinkling the group’s trademark orange powder on the square but not on the pitch.
Bairstow grabbed one of the demonstrators and carried them off the playing surface, with the other apprehended by stewards.
A third demonstrator was tackled before making it onto the outfield.
Spectators booed the protesters as they were led away by stewards.
Metropolitan Police later said that they had arrested three people.
Following a delay of several minutes while the orange powder was removed by ground-staff, play resumed with Broad bowling from the Nursery End.
Just Stop Oil, which wants an end to new oil and gas exploration in the North Sea, has disrupted a series of sporting events, including the British Formula One Grand Prix and Premiership rugby union final.
Protesters have tied themselves to goalposts during Premier League football matches and thrown orange powder on the green baize at the World Snooker Championship.
Just Stop Oil also delayed the England team bus taking the side to Lord’s for the lone Test against Ireland earlier this month.
A Just Stop Oil spokesperson said: “Cricket is an important part of our national heritage, but how can we enjoy England vs Australia when much of the cricketing world is becoming unfit for humans to live in?
“It’s time for cricket lovers and all those who understand the severity of this situation, to get onto the streets and demand action from this illegitimate, criminal government.”
Rishi Sunak’s spokesman said the UK Prime Minister was “pleased play was able to resume quickly and thanks security staff, the swift hands of Jonny Bairstow and other England players who stepped in”.
UK police forces were controversially granted new anti-protest powers by the government earlier this year following years of disruptive demonstrations by environmental activists.
“These sorts of selfish, guerrilla tactics that target events bringing joy to millions are exactly why the government brought in new powers so the police can take swift action,” Sunak’s spokesman added.
Marylebone Cricket Club chief executive Guy Lavender said he “condemns in the strongest possible terms” the action.